A Bayesian design criterion for locating the optimum point on a response surface

Most factorial experiments in industrial research form one stage in a sequence of experiments and so considerable prior knowledge is often available from earlier stages. A Bayesian A-optimality criterion is proposed for choosing designs, when each stage in experimentation consists of a small number of runs and the objective is to optimise a response. Simple formulae for the weights are developed, some examples of the use of the design criterion are given and general recommendations are made. (C) 2003 Elsevier B.V. All rights reserved.

Optimisation of high temperature puffing of potato cubes using response surface methodology

One cubic centimetre potato cubes were blanched, sulfited, dried initially for between 40 and 80 min in air at 90 degreesC in a cabinet drier, puffed in a high temperature fluidised bed and then dried for up to 180 min in a cabinet drier. The final moisture content was 0.05 dwb. The resulting product was optimised using response surface methodology, in terms of volume and colour (L-*, a(*) and b(*) values) of the dry product, as well as rehydration ratio and texture of the rehydrated product. The operating conditions resulting in the optimised product were found to be blanching for 6 min in water at 100 degreesC, dipping in 400 ppm sodium metabisulfite solution for 10 min, initially drying for 40 min and puffing in air at 200 degreesC for 40 s, followed by final drying to a moisture content of 0.05 dwb. (C) 2003 Elsevier Ltd. All rights reserved.

Effect of cutting time, temperature and calcium on curd moisture, whey fat loses and curd yield by response surface methodology

Response surface methodology was used to study the effect of temperature, cutting time, and calcium chloride addition level on curd moisture content, whey fat losses, and curd yield. Coagulation and syneresis were continuously monitored using 2 optical sensors detecting light backscatter. The effect of the factors on the sensors’ response was also examined. Retention of fat during cheese making was found to be a function of cutting time and temperature, whereas curd yield was found to be a function of those 2 factors and the level of calcium chloride addition. The main effect of temperature on curd moisture was to increase the rate at which whey was expelled. Temperature and calcium chloride addition level were also found to affect the light backscatter profile during coagulation whereas the light backscatter profile during syneresis was a function of temperature and cutting time. The results of this study suggest that there is an optimum firmness at which the gel should be cut to achieve maximum retention of fat and an optimum curd moisture content to maximize product yield and quality. It was determined that to maximize curd yield and quality, it is necessary to maximize firmness while avoiding rapid coarsening of the gel network and microsyneresis. These results could contribute to the optimization of the cheese-making process.

The importance of temperature and moisture to the egg-laying behaviour of a pest slug, Deroceras reticulatum

Oviposition behaviour is important when modelling the population dynamics of many invertebrates. The numbers of eggs laid are frequently used to describe fecundity, but this measure may differ significantly from realised fecundity. Oviposition has been shown to be important when describing the dynamics of slug populations, which are important agricultural pests. The numbers of eggs laid by Deroceras reticulatum and their viability were measured across a range of 16 temperature (4, 10, 15 and 23 degrees C) by moisture (33%, 42%, 53% and 58% by dry soil weight) experimental combinations. A fitted quadratic response surface model was used to estimate how D. reticulatum adjusted its egg laying to the surrounding temperature and moisture conditions, with most eggs being laid at a combination of 53% soil moisture and 18 degrees C. The number and proportion of viable eggs also covaried with temperature and moisture, suggesting that D. reticulatum may alter their investment in reproduction to maximise their fitness. We have shown that the number of viable eggs differs from the total number of eggs laid by D. reticulatum. Changes in egg viability with temperature and moisture may also be seen in other species and should be considered when modelling populations of egg-laying invertebrates.

Fitting models for the joint action of two drugs using SAS(R)

Combinations of drugs are increasingly being used for a wide variety of diseases and conditions. A pre-clinical study may allow the investigation of the response at a large number of dose combinations. In determining the response to a drug combination, interest may lie in seeking evidence of synergism, in which the joint action is greater than the actions of the individual drugs, or of antagonism, in which it is less. Two well-known response surface models representing no interaction are Loewe additivity and Bliss independence, and Loewe or Bliss synergism or antagonism is defined relative to these. We illustrate an approach to fitting these models for the case in which the marginal single drug dose-response relationships are represented by four-parameter logistic curves with common upper and lower limits, and where the response variable is normally distributed with a common variance about the dose-response curve. When the dose-response curves are not parallel, the relative potency of the two drugs varies according to the magnitude of the desired effect and the models for Loewe additivity and synergism/antagonism cannot be explicitly expressed. We present an iterative approach to fitting these models without the assumption of parallel dose-response curves. A goodness-of-fit test based on residuals is also described. Implementation using the SAS NLIN procedure is illustrated using data from a pre-clinical study. Copyright © 2007 John Wiley & Sons, Ltd.

Modelling climate impact on floods with ensemble climate projections

The evidence provided by modelled assessments of future climate impact on flooding is fundamental to water resources and flood risk decision making. Impact models usually rely on climate projections from global and regional climate models (GCM/RCMs). However, challenges in representing precipitation events at catchment-scale resolution mean that decisions must be made on how to appropriately pre-process the meteorological variables from GCM/RCMs. Here the impacts on projected high flows of differing ensemble approaches and application of Model Output Statistics to RCM precipitation are evaluated while assessing climate change impact on flood hazard in the Upper Severn catchment in the UK. Various ensemble projections are used together with the HBV hydrological model with direct forcing and also compared to a response surface technique. We consider an ensemble of single-model RCM projections from the current UK Climate Projections (UKCP09); multi-model ensemble RCM projections from the European Union's FP6 ‘ENSEMBLES’ project; and a joint probability distribution of precipitation and temperature from a GCM-based perturbed physics ensemble. The ensemble distribution of results show that flood hazard in the Upper Severn is likely to increase compared to present conditions, but the study highlights the differences between the results from different ensemble methods and the strong assumptions made in using Model Output Statistics to produce the estimates of future river discharge. The results underline the challenges in using the current generation of RCMs for local climate impact studies on flooding. Copyright © 2012 Royal Meteorological Society

Optimisation of oat milk formulation to obtain fermented derivatives by using probiotic Lactobacillus reuteri microorganisms

Functional advantages of probiotics combined with interesting composition of oat were considered as an alternative to dairy products. In this study, fermentation of oat milk with Lactobacillus reuteri and Streptococcus thermophilus was analysed to develop a new probiotic product. Central composite design with response surface methodology was used to analyse the effect of different factors (glucose, fructose, inulin and starters) on the probiotic population in the product. Optimised formulation was characterised throughout storage time at 4 ℃ in terms of pH, acidity, β-glucan and oligosaccharides contents, colour and rheological behaviour. All formulations studied were adequate to produce fermented foods and minimum dose of each factor was considered as optimum. The selected formulation allowed starters survival above 107/cfu ml to be considered as a functional food and was maintained during the 28 days controlled. β-glucans remained in the final product with a positive effect on viscosity. Therefore, a new probiotic non-dairy milk was successfully developed in which high probiotic survivals were assured throughout the typical yoghurt-like shelf life.

Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature. II. Different reconstructions of the total solar irradiance variation and dependence on response time scale

We have previously placed the solar contribution to recent global warming in context using observations and without recourse to climate models. It was shown that all solar forcings of climate have declined since 1987. The present paper extends that analysis to include the effects of the various time constants with which the Earth’s climate system might react to solar forcing. The solar input waveform over the past 100 years is defined using observed and inferred galactic cosmic ray fluxes, valid for either a direct effect of cosmic rays on climate or an effect via their known correlation with total solar irradiance (TSI), or for a combination of the two. The implications, and the relative merits, of the various TSI composite data series are discussed and independent tests reveal that the PMOD composite used in our previous paper is the most realistic. Use of the ACRIM composite, which shows a rise in TSI over recent decades, is shown to be inconsistent with most published evidence for solar influences on pre-industrial climate. The conclusions of our previous paper, that solar forcing has declined over the past 20 years while surface air temperatures have continued to rise, are shown to apply for the full range of potential time constants for the climate response to the variations in the solar forcings.

On the variability of the surface environment response to synoptic forcing over complex terrain: a multivariate data analysis approach

Synoptic climatology relates the atmospheric circulation with the surface environment. The aim of this study is to examine the variability of the surface meteorological patterns, which are developing under different synoptic scale categories over a suburban area with complex topography. Multivariate Data Analysis techniques were performed to a data set with surface meteorological elements. Three principal components related to the thermodynamic status of the surface environment and the two components of the wind speed were found. The variability of the surface flows was related with atmospheric circulation categories by applying Correspondence Analysis. Similar surface thermodynamic fields develop under cyclonic categories, which are contrasted with the anti-cyclonic category. A strong, steady wind flow characterized by high shear values develops under the cyclonic Closed Low and the anticyclonic H–L categories, in contrast to the variable weak flow under the anticyclonic Open Anticyclone category.

Assessment of surface winds over the Atlantic, Indian and Pacific Ocean sectors of the Southern Ocean in CMIP5 models: historical bias, forcing response, and state dependence

An assessment of the fifth Coupled Models Intercomparison Project (CMIP5) models’ simulation of the near-surface westerly wind jet position and strength over the Atlantic, Indian and Pacific sectors of the Southern Ocean is presented. Compared with reanalysis climatologies there is an equatorward bias of 3.7° (inter-model standard deviation of ± 2.2°) in the ensemble mean position of the zonal mean jet. The ensemble mean strength is biased slightly too weak, with the largest biases over the Pacific sector (-1.6±1.1 m/s, 27 -22%). An analysis of atmosphere-only (AMIP) experiments indicates that 41% of the zonal mean position bias comes from coupling of the ocean/ice models to the atmosphere. The response to future emissions scenarios (RCP4.5 and RCP8.5) is characterized by two phases: (i) the period of most rapid ozone recovery (2000-2049) during which there is insignificant change in summer; and (ii) the period 2050-2098 during which RCP4.5 simulations show no significant change but RCP8.5 simulations show poleward shifts (0.30, 0.19 and 0.28°/decade over the Atlantic, Indian and Pacific sectors respectively), and increases in strength (0.06, 0.08 and 0.15 m/s/decade respectively). The models with larger equatorward position biases generally show larger poleward shifts (i.e. state dependence). This inter-model relationship is strongest over the Pacific sector (r=-0.89) and insignificant over the Atlantic sector (r=-0.50). However, an assessment of jet structure shows that over the Atlantic sector jet shift is significantly correlated with jet width whereas over the Pacific sector the distance between the sub-polar and sub-tropical westerly jets appears to be more important.

The importance of surface pressure changes in the response of the atmosphere to zonally-symmetric thermal and mechanical forcing

he classical problem of the response of a balanced, axisymmetric vortex to thermal and mechanical forcing is re-examined, paying special attention to the lower boundary condition. The correct condition is DΦ/Dt = 0, where Φ is the geopotential and D/Dt the material derivative, which explicitly accounts for a mass redistribution as part of the mean-flow response. This redistribution is neglected when using the boundary condition Dp/Dt = 0, which has conventionally been applied in this problem. It is shown that applying the incorrect boundary condition, and thereby ignoring the surface pressure change, leads to a zonal wind acceleration δū/δt that is too strong, especially near the surface. The effect is significant for planetary-scale forcing even when applied at tropopause level. A comparison is made between the mean-flow evolution in a baroclinic life-cycle, as simulated in a fully nonlinear, primitive-equation model, and that predicted by using the simulated eddy fluxes in the zonally-symmetric response problem. Use of the correct lower boundary condition is shown to lead to improved agreement.

Response of El Niño sea surface temperature variability to greenhouse warming

The destructive environmental and socio-economic impacts of the El Niño/Southern Oscillation1, 2 (ENSO) demand an improved understanding of how ENSO will change under future greenhouse warming. Robust projected changes in certain aspects of ENSO have been recently established3, 4, 5. However, there is as yet no consensus on the change in the magnitude of the associated sea surface temperature (SST) variability6, 7, 8, commonly used to represent ENSO amplitude1, 6, despite its strong effects on marine ecosystems and rainfall worldwide1, 2, 3, 4, 9. Here we show that the response of ENSO SST amplitude is time-varying, with an increasing trend in ENSO amplitude before 2040, followed by a decreasing trend thereafter. We attribute the previous lack of consensus to an expectation that the trend in ENSO amplitude over the entire twenty-first century is unidirectional, and to unrealistic model dynamics of tropical Pacific SST variability. We examine these complex processes across 22 models in the Coupled Model Intercomparison Project phase 5 (CMIP5) database10, forced under historical and greenhouse warming conditions. The nine most realistic models identified show a strong consensus on the time-varying response and reveal that the non-unidirectional behaviour is linked to a longitudinal difference in the surface warming rate across the Indo-Pacific basin. Our results carry important implications for climate projections and climate adaptation pathways.

Climate response to basin-scale warming and cooling of the North Atlantic Ocean

Using experiments with an atmospheric general circulation model, the climate impacts of a basin-scale warming or cooling of the North Atlantic Ocean are investigated. Multidecadal fluctuations with this pattern were observed during the twentieth century, and similar variations--but with larger amplitude--are believed to have occurred in the more distant past. It is found that in all seasons the response to warming the North Atlantic is strongest, in the sense of highest signal-to-noise ratio, in the Tropics. However there is a large seasonal cycle in the climate impacts. The strongest response is found in boreal summer and is associated with suppressed precipitation and elevated temperatures over the lower-latitude parts of North and South America. In August­-September-­October there is a significant reduction in the vertical shear in the main development region for Atlantic hurricanes. In winter and spring, temperature anomalies over land in the extratropics are governed by dynamical changes in circulation rather than simply reflecting a thermodynamic response to the warming or cooling of the ocean. The tropical climate response is primarily forced by the tropical SST anomalies, and the major features are in line with simple models of the tropical circulation response to diabatic heating anomalies. The extratropical climate response is influenced both by tropical and higher-latitude SST anomalies and exhibits nonlinear sensitivity to the sign of the SST forcing. Comparisons with multidecadal changes in sea level pressure observed in the twentieth century support the conclusion that the impact of North Atlantic SST change is most important in summer, but also suggest a significant influence in lower latitudes in autumn and winter. Significant climate impacts are not restricted to the Atlantic basin, implying that the Atlantic Ocean could be an important driver of global decadal variability. The strongest remote impacts are found to occur in the tropical Pacific region in June­-August and September­-November. Surface anomalies in this region have the potential to excite coupled ocean­atmosphere feedbacks, which are likely to play an important role in shaping the ultimate climate response.

Land/sea warming ratio in response to climate change: IPCC AR4 model results and comparison with observations

Climate model simulations consistently show that in response to greenhouse gas forcing surface temperatures over land increase more rapidly than over sea. The enhanced warming over land is not simply a transient effect, since it is also present in equilibrium conditions. We examine 20 models from the IPCC AR4 database. The global land/sea warming ratio varies in the range 1.36–1.84, independent of global mean temperature change. In the presence of increasing radiative forcing, the warming ratio for a single model is fairly constant in time, implying that the land/sea temperature difference increases with time. The warming ratio varies with latitude, with a minimum in equatorial latitudes, and maxima in the subtropics. A simple explanation for these findings is provided, and comparisons are made with observations. For the low-latitude (40°S–40°N) mean, the models suggest a warming ratio of 1.51 ± 0.13, while recent observations suggest a ratio of 1.54 ± 0.09.